'Can' is fine grammatically-- or 'could' or 'might'-- but the question itself is an odd one in English (= western culture), where friendships grow gradually but tacitly from acquaintanceships. The direct question is seldom if ever asked.
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HimadriIf I ask someone for friendship what should I say "Can we become friends" , is "Can" is the right word here in this sentence. What are the other alternatives to ask for friendship.
Thanking you
Himadri Roy